Exponential and Logarithmic Equations Solve the equation. Find the exact solution if possible. otherwise, use a calculator to approximate to two decimals. log3(x−8)+log3x=2

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Exponential and Logarithmic Equations Solve the equation. Find the exact solution if possible. otherwise, use a calculator to approximate to two decimals.  log3(x−8)+log3x=2

krolaniaN · Accepted Answer

Step 1  For solving Exponential Equations:  1) Isolate the exponential expression on one side of the equation.  2) Take the logarithm of each side, then use the Laws of Logarithms to &quot;bring down exponent&quot;.  3) Solve for the variable.  Step 2  Given,  log3(x−8)+log3x=2  By the first law of logarithms function,  log3(x−8)x=2  By the definition of logarithm function,  logax=y⇔ ay=x  32=x(x−8)  9=x(x−8)  By the distributive property of multiplication,  x⋅ x−x⋅8=9  x2−8x=9  Add −9 on both sides,  x2−8x−9=9−9  x2−8x−9=0  Factor x2−8x−9 as (x−9)(x+1).  (x−9)(x+1)=0  By the zero-factor property,  x−9=0 and x+1=0  Taking,  x−9=0  Add 9 on both sides,  x−9+9=0+9  x=9  Now taking,  x+1=0  Add −1 on both sides,  x+1−1=0−1  x=−1  Here, we neglect x=−1 because logarithm function cannot be negative.  Thus, the exact solution is x=9.

Find the exact solution if possible: \log_{3}(x-8)+\log_{3}x=2

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